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rodikova [14]
4 years ago
14

Which of the following is a rational function?

Mathematics
1 answer:
Svetllana [295]4 years ago
6 0
The last one. F(x)=5x/x^2 - 25, because the first term is a fraction with polynomial numerator and denominator.
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Six plus a number is at least two times the number minus one
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A terrarium is built in the shape of a triangular prism. The prism is 10 inches in height and contains 450 cubic inches of space
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45 square inches

Step-by-step explanation:

We are told that a terrarium is constructed in a triangular prism shape with the following 10 inches tall and 450 cubic inches in volume.

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we solve for A:

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A = 45

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Not sure how I am supposed to arrive to an answer
ANEK [815]

Integrating both sides once gives

\dfrac{\mathrm d\mathbf r}{\mathrm dt}=2e^t\,\mathbf i+3e^{-t}\,\mathbf j+4e^{2t}\,\mathbf k+\mathbf c

where \mathbf c is an arbitrary constant vector. Use the initial condition to find its value:

\dfrac{\mathrm d\mathbf r}{\mathrm dt}(0)=-\mathbf i+7\,\mathbf j=(2+c_1)\,\mathbf i+(3+c_2)\,\mathbf j+(4+c_3)\,\mathbf k

\implies\mathbf c_1=-3\,\mathbf i+4\,\mathbf j-4\,\mathbf k

Integrate again:

\mathbf r(t)=2e^t\,\mathbf i-3e^{-t}\,\mathbf j+2e^{2t}\,\mathbf k+\mathbf c_1t+\mathbf c_2

where \mathbf c_2 is another arbitrary vector of constants. Use the other initial condition to determine its components:

\mathbf r(0)=6\,\mathbf i+\mathbf j+3\,\mathbf k=(2+c_1)\,\mathbf i+(-3+c_2)\,\mathbf j+(2+c_3)\,\mathbf k

\implies\mathbf c_2=4\,\mathbf i+4\,\mathbf j+\mathbf k

Then the particular solution to this ODE is

\boxed{\mathbf r(t)=(2e^t-3t+4)\,\mathbf i+(-3e^{-t}+4t+4)\,\mathbf j+(2e^{2t}-4t+1)\,\mathbf k}

5 0
3 years ago
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